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you're right, the answer is no... in fact, Bob can always block her from winning.this is one of those problems where you have to find the appropriate tiling. the one that works here is, divide the grid into 2x2 squares, then tile each 2x2 square with two dominoes, alternating horizontal and vertical tilings in a checkerboard pattern. then any group of 5 consecutive unit squares contains a complete domino, so all Bob has to do to block Alice is play an O in the same domino that Alice just played in: any 5 in a row that contain an X will also contain an O.
you're right, the answer is no... in fact, Bob can always block her from winning.
this is one of those problems where you have to find the appropriate tiling. the one that works here is, divide the grid into 2x2 squares, then tile each 2x2 square with two dominoes, alternating horizontal and vertical tilings in a checkerboard pattern. then any group of 5 consecutive unit squares contains a complete domino, so all Bob has to do to block Alice is play an O in the same domino that Alice just played in: any 5 in a row that contain an X will also contain an O.
